A team has finished a game with 14-0 singles and extra-base hits 266 times since 1897, most recently Cincinnati Reds on 31 August 2022. That is about one every 1,665 team-games.
Box score for the most recent one ↗
13-10 13-11 13-12 13-13 13-14 13-15 14-0 14-1 14-2 14-3 14-4 14-5 14-6
The whole distribution — Singles and Extra-Base Hits · All 18 shapes